Director of Cricket Mick Newell made Symonds an offer to act as cover for skipper Stephen Fleming when he captains New Zealand in Zimbabwe.
But Symonds has turned down the offer and Newell is now looking at alternative options.
He said: "We gave Symonds a deadline of this weekend because Fleming will be away from Trent Bridge in three and a half weeks and we needed a quick answer.
"With Symonds not selected for the Ashes he would have been a good replacement for Fleming in the middle order.
"But I will now be talking to other players to see if they are interested in filling the gap."
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